Problem 1: Cundh and cotrollr n the unity-c P(s) = s(s + 1)( C(s) = K s +10 , ) d) Now suppose that a time delay of T 1 sec is introduced to the system, i.e., the open-loop transfer-function G(s) is multiplied by the delay transfer-function Gd(s)-e Repeat the Bod plots in part (a) above. Note that the magnitude plot is not affected by the delay. The phase plot is shifted by a phase of LGd(jw)--wT. (With MATLAB, you can define the delayed open loop systemeG(s) by using 'Input Delay. You will notice that the phase rapidly decreases because T-1 sec is a huge amount of delay for this system. Use a smaller frequency range to zoom into the area where you can compare the phase crossover frequencies with and without delay.) e) Find the range of K for closed-loop stability using the Bod plots for the system with the time delay as in part (d). Is the maximum value of K for closed-loop stability larger for the system with or without the time delay? f) Find the estimated and the actual percent overshoot PO as in part (c) for the system with the time delay. Is the PO larger for the system with or without the time delay